Conventional methods for testing the mechanical properties of elastomeric materials, such as rubber and urethanes, seek to determine elastic and viscous moduli by vibrating specimens at different frequencies. For example, to find the elastic and loss bulk moduli of an elastomeric specimen with dimensions 5 inches in diameter and 1/2 inch in. thickness (circular disk-flat), these moduli should be functions of excitation frequency over a range of 0-2000 Hz.
As shown in FIG. 1A, a typical measuring technique is to use a Universal Test Machine (UTM) loading frame 10 to apply loads and capture data. The UTM 10 includes an upper crosshead 12 that supports a load cell 14 and is connected to a base crosshead 16, stably affixed to a floor mounted base 18. A flat disc specimen 20 is placed on top a hydraulic actuator 22, which imparts a forcing function to the specimen.
Using Fourier analysis, this forcing function can be regarded as comprising a range of excitation frequencies. The forcing function is measured by the load cell 14 as f(t). As seen in FIG. 1B, the load cell 14 measures time-varying input motions from a displacement x(t) in the specimen 20, in order to derive an elastic spring force proportionality rate k, and a viscous damping force proportionality rate c.
Forces generated and transmitted to the load cell are given as: EQU f(t)=cx+kx
A Fourier Transform to the frequency domain yields: EQU F(.omega.)=(k+j.omega.c)X(.omega.)
and a formulation of the Frequency Response Function (FRF): ##EQU1## PA1 shows that the real part represents the elastic spring rate and the imaginary part contains the damping rate times the frequency.
This method yields worthwhile results until f(t) begins to contain forces with sources other than those transmitted by the elastomer, for instance mechanical resonances of the machine parts. Results at frequencies above that point are unreliable. Dynamic force measurement (DFM) techniques may be used to remove the resonant effects from the f(t) data. However, neither method yields wide band frequency results directly.